Petitions were filed last night to recall Mayor Dennis J. Kucinich, one of the nation's youngest mayors at 31 and a man whose political credo is power to the people.

If there are 37,000 valid signatures among the more than 40,000 filed, a vote on Kucinich could be held by mid-summer, barring any court challenges. He has been in office only 166 days.

Ironically, Kucinich has used referendum and petition techniques to advance his own political causes during his 11-year career in City Hall.

To date, no Cleveland mayor has been recalled under the laborious provisions of the city charter. Attempts during the 1960s against Carl B. Stokes and Ralph Locher fizzled early.

Kucinich is the first big-city mayor in the nation to face a serious recall move since Philadelphia's Frank Rizzo, who appeared in deep political trouble in 1976 until the Pennsylvania Supreme Court ruled there were not enough valid signatures on the petition for a recall election.

The recall against Kucinich has thickened the storm clouds gathering over this troubled city, where in the fall the municipal government and school system face going broke at a time when a federal court busing order will go into effect.

City Council Clerk Mercedes Cotner will spend $10,000 and 10 days checking the signatures. If there are not 37,000 valid ones, the recall committee has 20 days to make up the difference.

Kucinich said the recall move is a hoax and was led by "my political enemies and crooks."

It was organized by supporters of state Rep. Edward F. Feighan, a Democrat, who lost to Kucinich in the November 1977 election by less than 3,000 votes out of 180,000 cast. They were assisted by several of Kucinich's enemies on the City Council and disgruntled neighborhood group activists.

The recall committee spent less than $2,000 and had no formal support from the Democratic and Republic party machines or powerful labor organizations.

The committee capitalized on the firestorm of protest that errupted last month over Kucinich's firing of Police Chief Richarf D. Hongisto, the one-time controversial sheriff of San Francisco.

The storm was fueled by a series of other zany events in City Hall that eroded public confidence in Kucinich - including a Watergate-style entry during the night into the office of a disloyal city executive.

The three political operatives, acting under orders from a Kucinich cabinet official, found no incriminating evidence as they ransacked his office. Instead, they drank his liquor and had a fist fight sometime during the night, according to police reports.

When City Council protested what several of them called "the Gestapolike tactics" of the raid, Kucinich retaliated by calling councilmen lunatics, buffoons and reactionaries.

At that point, several councilmen endorsed the recall while others, fearing retaliation from Kucinich, opposed him in private by turning over their own campaign aides to work for the recall committee.